Fuzzy rule based multiwavelet ECG signal denoising

Since different multiwavelets, pre- and post-filters have different impulse responses and frequency responses, different multiwavelets, pre- and post-filters should be selected and applied at different noise levels for signal denoising if signals are corrupted by additive white Gaussian noises. In this paper, some fuzzy rules are formulated for integrating different multiwavelets, pre- and post-filters together so that expert knowledge on employing different multiwavelets, pre- and post-filters at different noise levels on denoising performances is exploited. When an ECG signal is received, the noise level is first estimated. Then, based on the estimated noise level and our proposed fuzzy rules, different multiwavelets, pre- and post-filters are integrated together. A hard thresholding is applied on the multiwavelet coefficients. According to extensive numerical computer simulations, our proposed fuzzy rule based multiwavelet denoising algorithm outperforms traditional multiwavelet denoising algorithms by 30%

Spatio-temporal wavelet regularization for parallel MRI reconstruction: application to functional MRI

Parallel MRI is a fast imaging technique that enables the acquisition of highly resolved images in space or/and in time. The performance of parallel imaging strongly depends on the reconstruction algorithm, which can proceed either in the original k-space (GRAPPA, SMASH) or in the image domain (SENSE-like methods). To improve the performance of the widely used SENSE algorithm, 2D- or slice-specific regularization in the wavelet domain has been deeply investigated. In this paper, we extend this approach using 3D-wavelet representations in order to handle all slices together and address reconstruction artifacts which propagate across adjacent slices. The gain induced by such extension (3D-Unconstrained Wavelet Regularized -SENSE: 3D-UWR-SENSE) is validated on anatomical image reconstruction where no temporal acquisition is considered. Another important extension accounts for temporal correlations that exist between successive scans in functional MRI (fMRI). In addition to the case of 2D+t acquisition schemes addressed by some other methods like kt-FOCUSS, our approach allows us to deal with 3D+t acquisition schemes which are widely used in neuroimaging. The resulting 3D-UWR-SENSE and 4D-UWR-SENSE reconstruction schemes are fully unsupervised in the sense that all regularization parameters are estimated in the maximum likelihood sense on a reference scan. The gain induced by such extensions is illustrated on both anatomical and functional image reconstruction, and also measured in terms of statistical sensitivity for the 4D-UWR-SENSE approach during a fast event-related fMRI protocol. Our 4D-UWR-SENSE algorithm outperforms the SENSE reconstruction at the subject and group levels (15 subjects) for different contrasts of interest (eg, motor or computation tasks) and using different parallel acceleration factors (R=2 and R=4) on 2x2x3mm3 EPI images.Comment: arXiv admin note: substantial text overlap with arXiv:1103.353

Graph analysis of functional brain networks: practical issues in translational neuroscience

The brain can be regarded as a network: a connected system where nodes, or units, represent different specialized regions and links, or connections, represent communication pathways. From a functional perspective communication is coded by temporal dependence between the activities of different brain areas. In the last decade, the abstract representation of the brain as a graph has allowed to visualize functional brain networks and describe their non-trivial topological properties in a compact and objective way. Nowadays, the use of graph analysis in translational neuroscience has become essential to quantify brain dysfunctions in terms of aberrant reconfiguration of functional brain networks. Despite its evident impact, graph analysis of functional brain networks is not a simple toolbox that can be blindly applied to brain signals. On the one hand, it requires a know-how of all the methodological steps of the processing pipeline that manipulates the input brain signals and extract the functional network properties. On the other hand, a knowledge of the neural phenomenon under study is required to perform physiological-relevant analysis. The aim of this review is to provide practical indications to make sense of brain network analysis and contrast counterproductive attitudes

Empirical Bayes selection of wavelet thresholds

This paper explores a class of empirical Bayes methods for level-dependent threshold selection in wavelet shrinkage. The prior considered for each wavelet coefficient is a mixture of an atom of probability at zero and a heavy-tailed density. The mixing weight, or sparsity parameter, for each level of the transform is chosen by marginal maximum likelihood. If estimation is carried out using the posterior median, this is a random thresholding procedure; the estimation can also be carried out using other thresholding rules with the same threshold. Details of the calculations needed for implementing the procedure are included. In practice, the estimates are quick to compute and there is software available. Simulations on the standard model functions show excellent performance, and applications to data drawn from various fields of application are used to explore the practical performance of the approach. By using a general result on the risk of the corresponding marginal maximum likelihood approach for a single sequence, overall bounds on the risk of the method are found subject to membership of the unknown function in one of a wide range of Besov classes, covering also the case of f of bounded variation. The rates obtained are optimal for any value of the parameter p in (0,\infty], simultaneously for a wide range of loss functions, each dominating the L_q norm of the \sigmath derivative, with \sigma\ge0 and 0<q\le2.Comment: Published at http://dx.doi.org/10.1214/009053605000000345 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Wavelet Analysis and Denoising: New Tools for Economists

This paper surveys the techniques of wavelets analysis and the associated methods of denoising. The Discrete Wavelet Transform and its undecimated version, the Maximum Overlapping Discrete Wavelet Transform, are described. The methods of wavelets analysis can be used to show how the frequency content of the data varies with time. This allows us to pinpoint in time such events as major structural breaks. The sparse nature of the wavelets representation also facilitates the process of noise reduction by nonlinear wavelet shrinkage , which can be used to reveal the underlying trends in economic data. An application of these techniques to the UK real GDP (1873-2001) is described. The purpose of the analysis is to reveal the true structure of the data - including its local irregularities and abrupt changes - and the results are surprising.Wavelets, Denoising, Structural breaks, Trend estimation

A review of RFI mitigation techniques in microwave radiometry

Radio frequency interference (RFI) is a well-known problem in microwave radiometry (MWR). Any undesired signal overlapping the MWR protected frequency bands introduces a bias in the measurements, which can corrupt the retrieved geophysical parameters. This paper presents a literature review of RFI detection and mitigation techniques for microwave radiometry from space. The reviewed techniques are divided between real aperture and aperture synthesis. A discussion and assessment of the application of RFI mitigation techniques is presented for each type of radiometer.Peer ReviewedPostprint (published version